This material has been published in
J. Combin. Theory Ser. A
86
(1999), 103-126, the only definitive repository of the content that has been
certified and accepted after peer review. Copyright and all rights therein
are retained by Academic Press. This material may not be copied or reposted
without explicit permission.
Mihai Ciucu
and Christian Krattenthaler
The number of centered lozenge tilings of a symmetric hexagon
(19 pages)
Abstract.
Propp conjectured that the number of
lozenge tilings of a semiregular hexagon of sides 2n-1, 2n-1
and 2n
which contain the central unit rhombus is precisely one third of the total
number of lozenge tilings. Motivated by this, we consider the more general
situation of a semiregular hexagon of sides a, a and b. We prove
explicit formulas for the number of lozenge tilings of these hexagons
containing the central unit rhombus, and obtain Propp's conjecture as a
corollary of our results.
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